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Home , Calvin cycle, Hydrogen carrier, P680

Photosynthesis includes two main processes as PSII and PSI. The process is underpinned by the light- driven splitting reaction that occurs in PSII of plants, algae, and . Solar energy is absorbed by and other pigments and is transferred efficiently to the PSII reaction center where charge separation takes place. This initial conversion of light energy into electrochemical potential occurs in the reaction center of PSII with a maximum thermodynamic efficiency of about 70%. In principle, it could drive the formation of . Instead, the reducing equivalent is passed along an to PSI, where it is excited by the energy of a second ‘red’ photon absorbed by a chlorophyll . In this way, sufficient energy is accumulated to drive the fixation of dioxide, which not only requires the generation of the reduced ‘hydrogen carrier’, nicotinamide adenine dinucleotide (NADPH) but also the energy-rich molecule (ATP) formed by the release of some energy during electron transfer from PSII to PSI (in the form of an electrochemical potential gradient of protons)[1].

In the Calvin cycle, carbon from CO2 are fixed (incorporated into organic ) and used to build three-carbon sugars. This process is fueled by, and dependent on, ATP and NADPH from the light reactions. Unlike the light reactions, which take place in the membrane, the reactions of the Calvin cycle take place in the (the inner space of ). This process is shown in Figure S 1 and Figure S 2.

NADP+ CO2 Liquid water

Excited II Photosynthesis I NADPH+H+ Sunlight electrons Main product protons

Calvine cycle Waste(co- product)

ATP synthase

Biological process

Photon Exergy ADP+Pi Chemical exergy Electrical exergy

Gradient exergy

Figure S 1. Qualitative Exergy-Flow Diagram of the plant. The Color Key describes the type of exergy flows between the different biological operations[2]

Entropy 2021, 23, 3. https://dx.doi.org/10.3390/e23010003 www.mdpi.com/journal/entropy Entropy 2021, 23, 3. https://dx.doi.org/10.3390/e23010003 2 of 4

Figure S 2. Transfer of high energy electrons through II (PSII) and (PSI)[3]. Two chemical reactions are described in this figure. All of the reactions are explained here. In the first step, water is split into protons, oxygen, and electrons. The electrons are excited to the

high-level energy (P680*). NADPþ is reduced to NADPH. Intermediate carriers are various functional groups in the protein complexes of PSII and PSI.

The first assumption of the model is based on Table S 1:

Table S 1. The assumption for the average photon exergy

Parameter Unit Value

Avogadro’s number (NA) 6.023E+23

Planck’s Js 6.626E-34 constant (h) speed of ligh (c) m/s 300000000

λ_high(nm) nm 700

λ_low nm 400

T_earth(K) K 298.15

T_sun K 5762

B_photon_ave(kJ/mol photon) kJ/mol photon 212

Table S 2, Table S 3, Table S 4, and Table S 5 are the exergy analysis for photosynthesis and the Calvin cycle processes.

Table S 2. Exergies and reduction potentials of PSII

Redox standard Gibbs free standard change in Exergy Reactions potential energy change( electrical potential change (V) kJ/mol) (V) (J) 2𝐻𝑂→𝑂 +4𝐻 0.81 P680 1.1 -0.29 -671536 -819489

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P680(required -0.8 1.9 4399716 4399716 exergy from sun) Pheo -0.6 -0.2 -463128 -463128 Qa 0 -0.6 -1389384 -1389384 Qb 0.1 -0.1 -231564 -231564 Cytb 0.19 -0.09 -208408 -208408 PC 0.37 -0.18 -416815 -416815 total differernce 0.37 -0.44 1018882 870928

Table S 3. Exergies and reduction potentials of PS

Redox standard Gibbs free standard change in Exergy Reactions potential energy change electrical potential change (V) (kJ/mol) (V) (J) PC 0.37 P700 0.5 0.13 -301033 -301033 P700(required -1.3 -1.8 4168152 4168152 exergy from sun) A0 -1.3 -1.8 -694692 -694692 A1 -1 0.3 -486284 -486284 Fx -0.79 0.21 -138938 -138938 Fa -0.73 0.06 -324190 -324190 Fb -0.59 0.14 -92626 -92626 Fd -0.55 0.04 -46313 -46313 NADPH -0.53 0.02 -486284 -486284 total difference -0.32 0.21 1597792 1597792 total difference(NADPH -0.32 -1.13 2616173 2468720 -H2O)

Table S 4. Exergy losses in the dark reactions

Calvin Cycle reactions total exergy difference(δB(J)) 𝐶1: (𝑅𝑢5𝑃) + (𝐴𝑇𝑃) → (𝑅𝑢𝐵𝑃) +(𝐴𝐷𝑃) 98582

𝐶2: 𝐶𝑂 + (𝑅𝑢𝐵𝑃) +𝐻𝑂→2×(𝑃𝐺𝐴) 322242 𝐶3 + 𝐶4: (𝑃𝐺𝐴) + (𝐴𝑇𝑃) + (𝑁𝐴𝐷𝑃𝐻) → (𝐴𝐷𝑃) + (𝐺𝐴𝑙3𝑃) 32746 + (𝑁𝐴𝐷𝑃𝐻 ) +𝐻𝑃𝑂 𝐶5: (𝐺𝐴𝑙3𝑃) → (𝐷𝐻𝐴𝑃) 755 𝐶6: (𝐺𝐴𝑙3𝑃) +(𝐷𝐻𝐴𝑃)→(𝐹𝐵𝑃) 1974

𝐶7: (𝐹𝐵𝑃) +𝐻𝑂→(𝐹6𝑃) +𝐻𝑃𝑂 57933 𝐶8: (𝐹6𝑃) + (𝐺𝐴𝑙3𝑃) → (𝐸4𝑃) +(𝑋𝑢5𝑃) 6035 𝐶9: (𝐸4𝑃) +(𝐷𝐻𝐴𝑃)→(𝑆𝐵𝑃) 2023

𝐶10: (𝑆7𝑃) + (𝐺𝐴𝑙3𝑃) → (𝑆7𝑃) +𝐻𝑃𝑂 62498 𝐶11: (𝑆7𝑃) + (𝐺𝐴𝑙3𝑃) → (𝑅5𝑃) +(𝑋𝑢5𝑃) 11187 𝐶12: (𝑅5𝑃) → (𝑅𝑢5𝑃) 1289 𝐶13: (𝑋𝑢5𝑃) → (𝑅𝑢5𝑃) 766

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SUM 59803 conversion to glucose total exergy difference(δB(J)) 𝐶5∗: (𝐺𝐴𝑙3𝑃) → (𝐷𝐻𝐴𝑃) 189 𝐶6∗: (𝐷𝐻𝐴𝑃) + (𝐺𝐴𝑙3𝑃) → (𝐹𝐵𝑃) 987 ∗ 𝐶7 : (𝐹𝐵𝑃) +𝐻𝑂→(𝐹6𝑃) +𝐻𝑃𝑂 28966 𝐶14: (𝐹6𝑃) → (𝐺6𝑃) 1298

𝐶15: (𝐺6𝑃) +𝐻𝑂→(𝐺𝑙𝑢𝑐𝑜𝑠𝑒) +𝐻𝑃𝑂 31768 conversion to glucose SUM 63208 TOTAL SUM 661239

Table S 5. Overall efficiency

Inlet Outlet Loss Efficienc Overall PAR Reactions (kJ) (kJ) (kJ) y Loss(%) Loss(%) PAR Reflection 9977 9977 0 1 0 0 1322 1256 Non-PAR Reflection 661 0.05 61.33 6 4 Photosystem II 5319 4193 1126 0.788 5.5 14.45 absorption photosystem II ETC 5319 4074 1246 0.766 6.08 15.99 inlet photosystem I ETC 4209 2009 0.523 9.81 25.79 2200 ATP synthase 4901 2401 2500 0.49 12.2 32.09 Calvin cycle(Dark 1372 992 381 0.722 1.86 4.89 reaction)

References

[1] J. Barber, “Photosynthetic energy conversion: natural and artificial,” R. Soc. Chem. 2009, vol. 38, no. 1, pp. 185–196 |, 2009, doi: 10.1039/b802262n.

[2] C. S. Silva, W. D. Seider, and N. Lior, “Exergy efficiency of plant photosynthesis,” Chem. Eng. Sci., vol. 130, pp. 151–171, 2015, doi: 10.1016/j.ces.2015.02.011.

[3] M. M. C. David L. Nelson, Lehninger Principles of , Fourth Edi. W. H. Freeman, 2004.